By Frank Ayres Jr.
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Extra resources for Algebra moderna
Isabelle/Isar — a versatile environment for human-readable formal proof documents. PhD thesis, Institut f¨ ur Informatik, TU M¨ unchen (2002) Towards Constructive Homological Algebra in Type Theory Thierry Coquand1 and Arnaud Spiwack2 1 2 G¨ oteborg University Ecole Normale Sup´erieure de Cachan Abstract. This paper reports on ongoing work on the project of representing the Kenzo system  in type theory . Introduction This paper reports on ongoing work on the project of representing the system Kenzo  in type theory.
Context export destructs the logical diﬀerence of two contexts, by imposing it on local results. The eﬀect of export Γ 1 Γ 2 is to discharge portions of the context on terms and theorems as follows: export (Γ + fix x ) Γ (t x ) = (λx . t x ) export (Γ + fix x ) Γ ( B x ) =( x. B x) export (Γ + assume A) Γ (A B ) = ( A =⇒ B ) Discharging assumptions on syntactic terms has no eﬀect. 2 Context Data Isabelle belongs to the tradition of “LCF-style” provers, which is centered around formally checked entities being implemented as abstract datatypes.
1 (A, C) = Prove(A, C) is deﬁned iﬀ A is a set of syntactic formulas in Loop and C is a formula in Loop . It returns a syntactic representation of a proof if one exists. 2. π ˆ2 is the theorem proving process performed by some automated theorem prover. It takes the elements of A as assumptions and C as a conclusion. 3. M is P roves(Prove(A, C), A C) Here the predicate P roves checks the correctness of the derivation. The formalisation of this predicate depends on the calculus of the integrated prover and is generally very lengthy to formalise.
Algebra moderna by Frank Ayres Jr.